A. X = ABC +
A/.C = C (AB + A/)
B. Y = (Q + R)
(Q/+R/)
=Q.Q/ + Q.R/
+Q/.R +R.R/
=Q.R/+Q/.R
C. W = ABC +A.B/.C
+ A/
=AC (B+B/)
+A/
=AC +A/
=C + A/
D. Q = (RST)/.(R
+S+ T)/
=R/ +S/ +
T/. (R/.S/.T/)
=R/.S/.T/ +
R/.S/.T/ + R/.S/.T/
E. X= A/.B/.C/ +
A/.B.C +ABC+A.B/.C/+A.B/.
=B/.C/ (A/+A)
+ BC(A/+A) + A.B/.C
=B/.C/ + BC +
A.B/.C
=B/.C/ +
C(B+A.B/)
=B.C/ +
C(B+A)
=B.C/ +
B.C+A.C
=B+AC
F. Z = (
B+C/).(B/+C) +( A/+B+C/)/
=B.B/+BC +
B/.C/ + C/.C+(A//.B/.C//)
=BC + B/.C/
+A.B/.C
=BC +B/
(C/+AC)
=BC +
B/(C/+A)
=BC + B/.C/
+A.B/
G. Y= (C+D)/+
A/.C .D/ +A.B/.C/ +A/.B/.C.D + AC.D/
=C/.D/
+A/.C.D/ +AB/.C/ +A/.B/.CD + AC.D/
=D/(C/+A/C+AC) B/(AC/+A/CD)
=D/(C+D) B/
=D/C.B/
H. X = AB(C/.D)/ +
A/.B.D+B/.C/.D/
=AB(C+D/)
+A/.BD +B/.C/.D/
=ABC+AB.D/
+A/BD +B/.C/D/
=ABC + A/BD
+ D/(AB +B/C/)
=B/(AC+A/D)
+ D/(AB +B/C/)
4-6
A manufacturing plant needs to have a horn sound signal
quitting time. the horn sound should be activated when either the following is
met.
1. it's after 5 o'clock and all machines are shut down
2. it's Friday, the production run for day is complete, and
all machines are shut down
design the logic circuit that will control the horn (hint:
use for logic input variables to represent the various conditions. for examples
input A will be high only when the time
of the day is 5 o'clock or later..
ANSWER :
A = 5 O'CLOCK
B = MACHINES ARE SHUT DOWN
C = FRIDAY
D = PRODUCT IS COMPLETES
=A.B/ (C.D + C/.D) +
A/.B.C.D
=A.B/.D+A/.B.C.D
SOAL 4-49
1.
A/B/C/D/ + A/B/C/D + A/B/CD + A/B/CD/ + A/BC/D/ +
A/BC/D + ABCD/ + AB/CD + AB/CD/
=A/B/(C/D/+C/D+CD+CD/)
+ A/B(C/D/+C/D) + ABCD/ + AB/(CD+CD/)
=A/B/(C/+C) +
A/BC/ + ABCD/ + AB/C
=A/B/+A/BC/+ABCD/+AB/C
=A/(B/+BC/) +
ABCD/ + AB/C
=A/(B/+C/)
+ABCD/ + AB/C
=A/B/+A/C/+ABCD/+AB/C
=B/(A/+AC) +
A/C/ + ABCD/
=B/(A/+C) +
A/C/ + ABCD/
=B/A/ + B/C +
A/C/ + ABCD/
2. A/B/C/D/+A/B/CD+A/B/CD/+A/BC/D/+A/BCD/+AB/C/D/+AB/CD+AB/CD/
=A/B/(C/D/+CD+CD/)+A/B(C/D/+CD/)+AB/(C/D/+CD+CD/)
=A/B/(1+CD/)+ABD/+AB/(1+CD/)
=A/B/+A/B/CD/+ABD/+AB/(1+CD/)
=A/B/+A/B/CD/+ABD/+AB/+AB/CD/
=B/(A/+A/CD/)+A+ACD/)+ABD/
=B/(1+CD)+ABD/
=B/+B/CD+ABD/
=B/+ABD/
3. A/B/C+A/B/C+ABC/+AB/C/+AB/C
=C/(A/B/+AB+AB/)+C(A/B/+AB/)
=C/(1+AB/)+CB/
=C/+C/AB/+CB/
=C/+B/(C/A+C)
=C/+B/(C+A)
=C/+B/C+B/A
=C/+B/C+B/A
=C/+B+B/A
=C/+B+A
=C/(A/B/+AB+AB/)+C(A/B/+AB/)
=C/(1+AB/)+CB/
=C/+C/AB/+CB/
=C/+B/(C/A+C)
=C/+B/(C+A)
=C/+B/C+B/A
=C/+B/C+B/A
=C/+B+B/A
=C/+B+A
